Colored Point Cloud to Image Alignment

Recognition and segmentation of objects in images enjoy the wealth of large volume of well annotated data. At the other end, when dealing with the reconstruction of geometric structures of objects from images, there is a limited amount of accurate data available for supervised learning. One type of such geometric data with insufficient amount required for deep learning is real world accurate RGB-D images. The lack of accurate RGB-D datasets is one of the obstacles in the evolution of geometric scene reconstructions from images. One solution to creating such a dataset is to capture RGB images while simultaneously using an accurate depth scanning device that assigns a depth value to each pixel. A major challenge in acquiring such ground truth data is the accurate alignment between the RGB images and the measured depth and color profiles. We introduce a differential optimization method that aligns a colored point cloud to a given color image via iterative geometric and color matching. The proposed method enables the construction of RGB-D datasets for specific camera systems. In the suggested framework, the optimization minimizes the difference between the colors of the image pixels and the corresponding colors of the projected points to the camera plane. We assume that the colors produced by the geometric scanner camera and the color camera sensor are different and thus are characterized by different chromatic acquisition properties. We align the different color spaces while compensating for their corresponding color appearance. Under this setup, we find the transformation between the camera image and the point cloud colors by iterating between matching the relative location of the point cloud and matching colors. The successful alignments produced by the proposed method are demonstrated on both synthetic data with quantitative evaluation and real world scenes with qualitative results.

U-mesh: Human Correspondence Matching with Mesh Convolutional Networks

The proliferation of 3D scanning technology has driven a need for methods to interpret geometric data, particularly for human subjects. In this paper we propose an elegant fusion of regression (bottom-up) and generative (top-down) methods to fit a parametric template model to raw scan meshes. Our first major contribution is an intrinsic convolutional mesh U-net architecture that predicts pointwise correspondence to a template surface. Soft-correspondence is formulated as coordinates in a newly-constructed Cartesian space. Modeling correspondence as Euclidean proximity enables efficient optimization, both for network training and for the next step of the algorithm. Our second contribution is a generative optimization algorithm that uses the U-net correspondence predictions to guide a parametric Iterative Closest Point registration. By employing pre-trained human surface parametric models we maximally leverage domain-specific prior knowledge. The pairing of a mesh-convolutional network with generative model fitting enables us to predict correspondence for real human surface scans including occlusions, partialities, and varying genus (e.g. from self-contact). We evaluate the proposed method on the FAUST correspondence challenge where we achieve 20% (33%) improvement over state of the art methods for inter- (intra-) subject correspondence.

Provably Approximated ICP

The goal of the \emph{alignment problem} is to align a (given) point cloud $P = \{p_1,\cdots,p_n\}$ to another (observed) point cloud $Q = \{q_1,\cdots,q_n\}$. That is, to compute a rotation matrix $R \in \mathbb{R}^{3 \times 3}$ and a translation vector $t \in \mathbb{R}^{3}$ that minimize the sum of paired distances $\sum_{i=1}^n D(Rp_i-t,q_i)$ for some distance function $D$. A harder version is the \emph{registration problem}, where the correspondence is unknown, and the minimum is also over all possible correspondence functions from $P$ to $Q$. Heuristics such as the Iterative Closest Point (ICP) algorithm and its variants were suggested for these problems, but none yield a provable non-trivial approximation for the global optimum. We prove that there \emph{always} exists a "witness" set of $3$ pairs in $P \times Q$ that, via novel alignment algorithm, defines a constant factor approximation (in the worst case) to this global optimum. We then provide algorithms that recover this witness set and yield the first provable constant factor approximation for the: (i) alignment problem in $O(n)$ expected time, and (ii) registration problem in polynomial time. Such small witness sets exist for many variants including points in $d$-dimensional space, outlier-resistant cost functions, and different correspondence types. Extensive experimental results on real and synthetic datasets show that our approximation constants are, in practice, close to $1$, and up to x$10$ times smaller than state-of-the-art algorithms.

Abiotic Stress Prediction from RGB-T Images of Banana Plantlets

Prediction of stress conditions is important for monitoring plant growth stages, disease detection, and assessment of crop yields. Multi-modal data, acquired from a variety of sensors, offers diverse perspectives and is expected to benefit the prediction process. We present several methods and strategies for abiotic stress prediction in banana plantlets, on a dataset acquired during a two and a half weeks period, of plantlets subject to four separate water and fertilizer treatments. The dataset consists of RGB and thermal images, taken once daily of each plant. Results are encouraging, in the sense that neural networks exhibit high prediction rates (over $90\%$ amongst four classes), in cases where there are hardly any noticeable features distinguishing the treatments, much higher than field experts can supply.

A Color Elastica Model for Vector-Valued Image Regularization

Models related to the Euler's Elastica energy have proven to be very useful for many applications, including image processing and high energy physics. Extending the Elastica models to color images and multi-channel data is challenging, as numerical solvers for these geometric models are difficult to find. In the past, the Polyakov action from high energy physics has been successfully applied for color image processing. Like the single channel Euler's elastica model and the total variation (TV) models, measures that require high order derivatives could help when considering image formation models that minimize elastic properties, in one way or another. Here, we introduce an addition to the Polyakov action for color images that minimizes the color manifold curvature, that is computed by applying of the Laplace-Beltrami operator to the color image channels. When applied to gray scale images, while selecting appropriate scaling between space and color, the proposed model reduces to minimizing the Euler's Elastica operating on the image level sets. Finding a minimizer for the proposed nonlinear geometric model is the challenge we address in this paper. Specifically, we present an operator-splitting method to minimize the proposed functional. The nonlinearity is decoupled by introducing three vector-valued and matrix-valued variables. The problem is then converted into solving for the steady state of an associated initial-value problem. The initial-value problem is time-split into three fractional steps, such that each sub-problem has a closed form solution, or can be solved by fast algorithms. The efficiency, and robustness of the proposed method are demonstrated by systematic numerical experiments.

LIMP: Learning Latent Shape Representations with Metric Preservation Priors

In this paper, we advocate the adoption of metric preservation as a powerful prior for learning latent representations of deformable 3D shapes. Key to our construction is the introduction of a geometric distortion criterion, defined directly on the decoded shapes, translating the preservation of the metric on the decoding to the formation of linear paths in the underlying latent space. Our rationale lies in the observation that training samples alone are often insufficient to endow generative models with high fidelity, motivating the need for large training datasets. In contrast, metric preservation provides a rigorous way to control the amount of geometric distortion incurring in the construction of the latent space, leading in turn to synthetic samples of higher quality. We further demonstrate, for the first time, the adoption of differentiable intrinsic distances in the backpropagation of a geodesic loss. Our geometric priors are particularly relevant in the presence of scarce training data, where learning any meaningful latent structure can be especially challenging. The effectiveness and potential of our generative model is showcased in applications of style transfer, content generation, and shape completion.

Do We Need Depth in State-Of-The-Art Face Authentication?

Some face recognition methods are designed to utilize geometric features extracted from depth sensors to handle the challenges of single-image based recognition technologies. However, calculating the geometrical data is an expensive and challenging process. Here, we introduce a novel method that learns distinctive geometric features from stereo camera systems without the need to explicitly compute the facial surface or depth map. The raw face stereo images along with coordinate maps allow a CNN to learn geometric features. This way, we keep the simplicity and cost efficiency of recognition from a single image, while enjoying the benefits of geometric data without explicitly reconstructing it. We demonstrate that the suggested method outperforms both existing single-image and explicit depth based methods on large-scale benchmarks. We also provide an ablation study to show that the suggested method uses the coordinate maps to encode more informative features.

The Whole Is Greater Than the Sum of Its Nonrigid Parts

According to Aristotle, a philosopher in Ancient Greece, "the whole is greater than the sum of its parts". This observation was adopted to explain human perception by the Gestalt psychology school of thought in the twentieth century. Here, we claim that observing part of an object which was previously acquired as a whole, one could deal with both partial matching and shape completion in a holistic manner. More specifically, given the geometry of a full, articulated object in a given pose, as well as a partial scan of the same object in a different pose, we address the problem of matching the part to the whole while simultaneously reconstructing the new pose from its partial observation. Our approach is data-driven, and takes the form of a Siamese autoencoder without the requirement of a consistent vertex labeling at inference time; as such, it can be used on unorganized point clouds as well as on triangle meshes. We demonstrate the practical effectiveness of our model in the applications of single-view deformable shape completion and dense shape correspondence, both on synthetic and real-world geometric data, where we outperform prior work on these tasks by a large margin.

Bilateral Operators for Functional Maps

A majority of shape correspondence frameworks are based on devising pointwise and pairwise constraints on the correspondence map. The functional maps framework allows for formulating these constraints in the spectral domain. In this paper, we develop a functional map framework for the shape correspondence problem by constructing pairwise constraints using point-wise descriptors. Our core observation is that, every point-wise descriptor allows for the construction a pairwise kernel operator whose low frequency eigenfunctions depict regions of similar descriptor values at various scales of frequency. By aggregating the pairwise information from the descriptor and the intrinsic geometry of the surface encoded in the heat kernel, we construct a hybrid kernel and call it the bilateral operator. Analogous to the edge preserving bilateral filter in image processing, the action of the bilateral operator on a function defined over the manifold yields a descriptor dependent local smoothing of that function. By forcing the correspondence map to commute with the Bilateral operator, we show that we can maximally exploit the information from a given set of pointwise descriptors in a functional map framework.